Question

The distance moved by a freely falling body (starting from rest) during the $1^{st},2^{nd}$ and $3^{rd}...n^{th}$ second of its motion, are proportional to

• A. $(n-1)$
• B. $(2n-1)$
• C. $(n^2-1)$
• D. $(2n-1)/n^2$

Answer 1

The correct option is B $(2n-1)$

Distance travelled by body in $n^{th}$ second;
$s_n-s_{n-1}=u(n-(n-1\left)\right)-\frac{1}{2}g[n^2-(n-1{)}^2]$

$s_n-s_{n-1}=\frac{-g}{2}(2n-1)$

$s_n-s_{n-1}\propto (2n-1)$